AbstractPrecision experiments, such as the search for electric dipole
moments of charged particles using radiofrequency spin rotators in storage
rings, demand for maintaining the exact spin resonance condition for several
thousand seconds. Synchrotron oscillations in the stored beam modulate the
spin tune of off-central particles, moving it off the perfect resonance
condition set for central particles on the reference orbit. Here we report an
analytic description of how synchrotron oscillations lead to non-exponential
decoherence of the radiofrequency resonance driven up-down spin rotations.
This non-exponential decoherence is shown to be accompanied by a nontrivial
walk of the spin phase. We also comment on sensitivity of the decoherence
rate to the harmonics of the radiofreqency spin rotator and a possibility to
check predictions of decoherence-free magic energies.